Friday, 29 June 2012

The latest issue of The Reasoner is out, and among other interesting features, it has an interview with the cognitive scientist Keith Stenning, conducted by me. Keith is (in my opinion) the sharpest, most interesting researcher currently working on reasoning, so everyone should be thoroughly familiar with his work! He has two fairly recent can't-miss books, Seeing Reason and (with Michiel van Lambalgen) Human Reasoning and Cognitive Science. In the interview, he talks about the status of cognitive science and psychology as disciplines, his interdisciplinary professional trajectory, and his recent collaboration with Michiel van Lambalgen tracking down the inherent component of defeasibility in human reasoning.

Thursday, 21 June 2012

This week I read an extremely interesting paper by Kenny Easwaran, ‘Probabilistic proofs and transferability’, which appeared in Philosophia Mathematica in 2009. Kenny had heard me speak at the Formal Epistemology Workshop in Munich a few weeks ago, and thought (correctly!) that there were interesting connections between the concept of transferability that he develops in the paper and my ‘built-in opponent’ conception of logic and deductive proofs; so he kindly drew my attention to his paper. Because I believe Kenny is really on to something deep about mathematics in his paper, I thought it would be a good idea to elaborate a bit on these connections in a blog post, hoping that it will be of interest to a number of people besides the two of us!

Drawing on previous work by Don Fallis, Kenny’s paper addresses the issue of why probabilistic proofs are for the most part not regarded as ‘real proofs’ by mathematicians, even though some of them can be said to have a higher degree of certainty than very long traditional proofs (given that in very long proofs, the probability of a mistake being made somewhere is non-negligible). He discusses in particular the Miller-Rabin primality test. (I recall having heard Michael Rabin speaking on this twice some years ago, and recall being both extremely impressed and extremely puzzled by what he was saying!) But for the full story, you’ll just have to read Kenny’s paper, as here I will focus on his concept of transferability so as to compare it to the built-in opponent conception of proofs that I am currently developing.

Kenny’s main claim is that, even if they offer a very high degree of epistemic certainty (in some sense), these probabilistic proofs lack the feature of transferability, and this is why they are not accepted as ‘proper proofs’ by most mathematicians. Thus, he proposes transferability as the ultimate conceptual core of the conception of proofs that mathematicians de facto entertain. Here is how he presents the concept of transferability:

… the basic idea is that a proof must be such that a relevant expert will become convinced of the truth of the conclusion of the proof just by consideration of each of the steps in the proof. With non-transferable proofs, something extra beyond just the steps in the proof is needed—in the case of probabilistic proofs, this extra component is a knowledge of the process by which the proof was generated, and in particular that the supposedly random steps really were random.

As he soon adds, “transferability is a social epistemic virtue, rather than an individual one.” A transferable proof is one which can be checked by any expert mathematician (possibly within a given mathematical subfield). Importantly, when checking a proof, a mathematician adopts what can be described as an adversarial attitude towards the author of the proof: she will scrutinize every step looking for loops in the argumentation, in particular counterexamples to specific inferential steps. Once she runs through the proof and finds no fault in it, she is persuaded of the truth of the conclusion if she has granted the premises. Thus, on this conception, a proof is a public discourse aimed at persuasion; this also explains why mathematicians prefer proofs that are not only correct, but which are also explanatory: their persuasive effect is greater.

As Kenny correctly noted, his notion of transferability is very closely related to my ‘built-in opponent’ (BIO) hypothesis. I recall having mentioned BIO in blog posts before (and see here for a draft paper), but here is a recap: I rely on the historical development of the deductive method (as documented in e.g. Netz’s The Shaping of Deduction) to argue that a deductive argument is originally a discourse aimed at compelling the audience to accept (the truth of) the conclusion, if they accept (the truth of) the premises. It is only in the modern period, in particular with Descartes and Kant, that logic became predominantly associated with inner thinking processes rather than with public situations of dialogical interaction.

Crucially, deductive proofs would correspond to a specific kind of dialogues, namely adversarial dialogues of a very special kind, as the participants have opposite goals: proponent seeks to establish the conclusion; opponent seeks to block the establishment of the conclusion. But deductive proofs are no longer dialogues properly speaking, as they do not correspond to actual dialogical interactions between two or more active participants. In effect, the two main transformations leading from the actual dialogues of the early Academy (which provided the historical background for the emergence of the notion of a deductive argument) to deductive proofs seem to be the move from oral to written contexts, and the fact that the deductive method has internalized the opponent in the sense that it is now built into the framework: every inferential step must be immune to counterexamples, i.e. it must be indefeasible. I refer to this conception as the built-in opponent conception of proofs because the original role of opponent (checking whether the dialogical moves made by proponent are indefeasible) is now played by the method itself, so to speak: the method has become the idealized opponent. Another way of formulating the same point is to say that what started out as a strategic desideratum (the formulation of indefeasible arguments) then became a constitutive feature of the method as such.

It should be clear by now how closely related Kenny’s notion of transferability and my BIO conception are. For starters, we both emphasize the social nature of a deductive proof as a discourse aimed at persuasion, which must thus be ‘transferable’. Indeed, Kenny discusses at length the fact that, in mathematics, testimony is not a legitimate source of information/knowledge (contrasting with how widely testimony is relied upon for practical purposes and even in other scientific domains*): the mathematician “will want to convince herself of everything and avoid trusting testimony.” I believe that the key point to understand the absence of testimony in mathematics is the adversarial nature of the dialogues having given rise to the deductive method: your opponent in such a dialogical interaction is by definition not trustworthy. However, in a probabilistic proof, she who surveys the proof must trust that the author of the proof did not cherry-pick the witnesses, which is at odds with the idea of mathematical proofs as corresponding to adversarial dialogues.

Moreover, the dialogical model explains why, in a mathematical proof, one is allowed to use only information that is explicitly accepted. In Kenny’s terms:

Papers will rely only on premises that the competent reader can be assumed to antecedently believe, and only make inferences that the competent reader would be expected to accept on her own consideration. If every proof is published in a transferable form, then the arguments for any conclusion are always publicly available for the community to check.

This is because the premises in a mathematical proof are the propositions that all participants in the dialogue in question (proponent, opponent and audience) have explicitly granted: no recourse to external, contentious information is allowed.

But the upshot is that, while ultimately based on an adversarial dialogical model, it is precisely the constant self-monitoring made possible by the transferability of proofs that makes mathematics a social, collective enterprise as well as an astonishingly fruitful field of inquiry: it allows for a sort of cooperative division of labor (distributed cognition!). Recall when Edward Nelson announced he had a proof of the inconsistency of PA last year: the mathematical community immediately joined forces to scrutinize his (purported) proof, thus adopting the adversarial role of opponent (in my terminology). Before long, Terry Tao found a loop in the proof (see comments in this post, where Tao describes his train of thought); and once he was convinced of the cogency of Tao’s argument, Nelson gracefully withdrew his claim.

I also want to suggest that the social nature of mathematics makes Bayesianism, originally an individualistic framework, ultimately unsuitable to deal with the epistemology of mathematics. But as this post is already much too long, I will not further develop this idea for now. Indeed, these are just some preliminary reflections on the connections between the concepts of transferability and of a ‘built-in opponent’ in a deductive proof; I hope to give all this much more thought in the coming months, but for now I’d be curious to hear what others may have to say on all this.

----------------------------------------------------------------------
* I suspect that transferability in mathematics does have a counterpart in the empirical sciences, namely replication of experimental results, but this will remain a topic for another post.

The application of formal tools from logic and rational choice theory to the analysis of ethicalconcepts and theories is a rapidly growing field of research. It has shed new light on a variety ofconcepts that are central to ethical theory, such as freedom, responsibility, values, norms, andconventions. We invite submissions to Formal Ethics 2012, to be held at the Munich Center forMathematical Philosophy on October 11th to 13th, 2012. The workshop aims to bring togetherresearchers at the crossroads of ethical theory and formal methods.

Aside from the contributed talks, the workshop will feature keynote addresses from:

*Instruction for submission:*Authors should send an extended abstract (1000 words max, pdf or postscript format) together withtheir name, institutional affiliation(s) and current position(s) to the Organizing Committee([log in to unmask]) with the mention "Submission" in the email topic.

*Travel grants for graduate students:*We especially encourage graduate students to submit. A number of travel grants for up to 500 Euroare available. If you want to apply for a grant, please say so in your submission.

Monday, 18 June 2012

The Chair of Philosophy of Science (Professor Stephan Hartmann) at the Faculty of Philosophy, Philosophy of Science and Study of Religion and the Munich Center for Mathematical Philosophy (MCMP) at Ludwig-Maximilians-University Munich (LMU) seek applications for the following positions:

The Chair of Philosophy of Science focuses on general philosophy of science and the philosophy of the natural and social sciences. We are especially interested in conducting joint research projects with colleagues from other faculties at LMU and elsewhere.
The MCMP is devoted to applications of logical, mathematical, and computational methods in philosophy. It was established in 2010 and is generously supported by the Alexander von Humboldt Foundation through two Alexander von Humboldt professorships. Directed by Professor Stephan Hartmann and Professor Hannes Leitgeb, who founded the MCMP, the MCMP hosts a vibrant research community of university faculty, postdoctoral fellows, doctoral fellows, master students, and visiting fellows. The MCMP organizes at least two weekly colloquia and a weekly internal work in-progress seminar, as well as various other activities such as workshops, conferences, and reading groups. For more information, seehttp://www.mcmp.philosophie.uni-muenchen.de/index.html
The official language at the Chair and at the MCMP is English and fluency in German is not mandatory.
We especially encourage female scholars to apply. The LMU in general, and the Chair of Philosophy of Science and the MCMP in particular, endeavor to raise the percentage of women among its academic personnel. Furthermore, given equal qualification, severely physically challenged individuals will be preferred.

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1. Three Assistant Professorships
Candidates are expected to have the following areas of specialization. Position 1: Philosophy of science with an emphasis in the philosophy of physics. Position 2: Philosophy of science with an emphasis in the philosophy of psychology and/or the social sciences and/or economics. Position 3: Modeling and simulation in philosophy. The areas of competence are open.
The positions are for three years with the possibility of extension. The appointment will be made within the German A13 salary scheme (under the assumption that the civil service requirements are met), which means that one has the rights and perks of a civil servant. The starting date is October 1, 2012, but a later starting date is also possible. (Please let us know if you wish to start at a later date.)
The appointee will be expected (i) to do philosophical research in the specified AOS and lead the respective group, (ii) to teach five hours a week in philosophy of science and/or a related field, and (iii) to take on management tasks. The successful candidate will have a PhD in philosophy and teaching experience in philosophy.
Applications (including a cover letter that addresses, amongst others, one's academic background and research interests, CV, certificates, list of publications, a sample of written work, and a 3-page description of planned research projects) should be sent to

by July 18, 2012. Please indicate for which of the three position you apply and let us know whether or not you are also considering a Postdoctoral Fellowship (see below). Applications by email are much preferred (ideally with everything requested in one PDF document). Additionally, two confidential letters of reference addressing the applicant's qualifications for academic research should be sent to the same address from the referees directly.
Contact for informal inquiries: Professor Stephan Hartmann (S.Hartmann@gmail.com)

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2. Six Postdoctoral Fellowships
The successful candidates will partake in all of MCMP's academic activities and enjoy its administrative facilities and financial support. In this round of advertisements, we are especially interested in candidates who work in the following areas: general philosophy of science (formal and non-formal), philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of economics, formal epistemology, social epistemology (formal and non-formal), individual and collective decision theory, modeling and simulation in philosophy, and experimental philosophy, but we are also open to candidates who apply formal methods in metaphysics, moral and political philosophy or any other part of philosophy.
The fellowships are open for candidates with a PhD in philosophy as well as for candidates with a PhD in a natural or social science who have foundational and/or methodological research interests (please explain in the letter). The postdoctoral stipends are for three years, and they should be taken up by October 1, 2012, but a later starting date is also possible. (Please let us know if you wish to start at a later date.) Each stipend will amount to EUR 2400 of monthly salary (normally tax-free, but excluding insurance). Additionally, the MCMP helps its fellows with the costs that arise from attending conferences (fees, traveling, accommodation). There is the possibility, though no obligation, to do some teaching in either English or German.
Applications (including a cover letter that addresses, amongst others, one's academic background and research interests, CV, certificates, list of publications, a sample of written work, and a 3-page description of a planned research project) should be sent to

by July 18, 2012. Applications by email are much preferred (ideally with everything requested in one PDF document). Additionally, two confidential letters of reference addressing the applicant's qualifications for academic research should be sent to the same address from the referees directly.
Contact for informal inquiries: Professor Stephan Hartmann (S.Hartmann@gmail.com)

--------------------
3. Six Doctoral Fellowships
The successful candidates will partake in all of MCMP's academic activities and enjoy its administrative facilities and financial support. In this round of advertisements, we are especially interested in candidates who work in the following areas: general philosophy of science (formal and non-formal), philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of economics, formal epistemology, social epistemology (formal and non-formal), individual and collective decision theory, modeling and simulation in philosophy, and experimental philosophy, but we are also open to candidates who apply formal methods in metaphysics, moral and political philosophy or any other part of philosophy.
The fellowships are open for candidates with a master degree in philosophy as well as for candidates with a master degree in a natural or social science who have foundational and/or methodological research interests (please explain in the letter).The doctoral stipends are for three years at the end of which the fellows are expected to have finished their PhD thesis. The fellowships should be taken up by October 1, 2012, but a later starting date is also possible. (Please let us know if you wish to start at a later date.) Each stipend will amount to EUR 1500 of monthly salary (normally tax-free, but excluding insurance). Additionally, the MCMP helps its fellows with the costs that arise from attending conferences (fees, traveling, accommodation).
Applications (including a cover letter that addresses, amongst others, one's academic background and research interests, CV, certificates, list of publications, a sample of written work, and a 3-page description of a planned research project) should be sent to

by July 18, 2012. Applications by email are much preferred (ideally with everything requested in one PDF document). Additionally, two confidential letters of reference addressing the applicant's qualifications for doctoral research should be sent to the same address from the referees directly.
Contact for informal inquiries: Professor Stephan Hartmann (S.Hartmann@gmail.com)

Wednesday, 13 June 2012

In this post, I’m going
to continue my crusade against certain revisionist approaches to logic in
response to paradoxes, which I consider to be insufficiently motivated. I’ve
talked about some of my objections in a few previous posts (here for example), but the main point
is ultimately that any rejection of a rule of inference or structural rule on
the grounds that ‘it leads to paradox’ seems to me to require additional, independent
motivation. Let me hasten to add that I have no particular fondness for
classical logic, and thus my critique is not motivated by general
anti-revisionist inclinations. But I am suspicious of what can be described as
‘fix-up’ solutions, which among other things sidestep the opportunity of
engaging in serious reflection on the exact nature of paradoxical phenomena,
and what they tell us about some of our most basic logical concepts.

Currently, a popular
revisionist strategy is to go substructural: rather than ‘ditching’ one of the
usual rules of inference (say, modus ponens), what has to go is one of the
plausible structural principles underlying (often tacitly) classical logic and many
other logical systems. In particular, recently the rule of contraction has been presented as the paradoxical culprit by
several people such as JC Beall, Elia Zardini and Ole Hjorland, who then go on
to argue in favor of contraction-free logical systems, or else for restrictions
on contraction. Contraction is the rule that says that, if you can infer C from
A, A and B, then you can infer C from A and B: the number of occurrences of
copies of a given premise is irrelevant for validity. In natural deduction
settings, this means that one can assume a given formula as many times as one
wants, and then discharge all the assumptions in one go, with just one
application of implication introduction.

It is argued that many (if
not all) derivations of paradoxes, such as the Liar or Curry, make crucial use
of multiple discharge, and thus of the structural rule of contraction. See for
example this derivation of Curry’s paradox (borrowed from a draft paper by Ole Hjortland - sorry for the terrible resolution!):

The key point is that, both on
the right branch and on the left branch, two occurrences of the assumption
[T<C>] are discharged with one occurrence on each side of implication
introduction. To be sure, it is certainly an interesting observation that
contraction seems to be involved in all these paradoxical derivations, but is
this enough to justify rejecting and/or restricting contraction with no further
argumentation? I submit that it is not.

What could count as a more robust
argument against contraction, beyond the observation that it seems to be
involved in typical derivations of logical paradoxes such as the Liar and
Curry? As I see it, the question to be asked is: what made us think that contraction was a plausible principle in the
first place? If we can go back to the original reasons to endorse
contraction and find fault in them, then we might have independent motivation
to reject the principle, other than the fact that it seems to be involved in
paradoxical derivations. Either way, this is an opportunity to reflect
critically on some of the very building blocks of our conception of logic.

Now, if necessary
truth-preservation is both a necessary and sufficient condition for validity,
it is hard to see what could possibly be wrong with contraction: if A, A, B
=> C is a valid consequence, then so is A, B => C, as the collection of
premises {A, A, B} is verified by exactly the same situations as the collection
of premises {A, B}. Similarly, on the dialogical conception of logic that I’ve
been developing recently, once a premise A has been stated and accepted by the
participants in the dialogical game in question, participants (proponent in
particular) can help themselves to A as many times as they wish: it becomes a commonly
owned and permanently available commodity as it were (it doesn’t ‘wear out’).

In my opinion, the thus far most
convincing rejection of contraction is the one of linear logic, which, as a
logic of resources, is sensitive to the number of copies of a given formula
available: once used, the particular copy of the formula is no longer
available. There may be other plausible reasons why a given logic will be
sensitive to resources in this way, e.g. some logics of information. But these
are all independent motivations to reject or restrict contraction, unrelated to
paradoxes.

But specifically with respect to
paradoxes, an interesting avenue to be pursued might be to investigate what
exactly is problematic about the particularoccurrences of contraction in the paradoxical
derivations in question. At the Q&A after Ole’s talk last week at the FLC
conference in St. Andrews, Peter Schroeder-Heister made an interesting observation:
as it turns out, in every case of multiple discharge in these paradoxical
derivations, the two (or more) occurrences of a given formula are heterogeneous
in that one is assumed and then undergoes an application, while the other is
simply assumed. This can be observed in the derivation above: in both branches,
the first assumption of [T<C>] is then ‘developed’ into C, and
subsequently into [T<C>] à
p (which is by definition what C means), while the second assumption of
[T<C>] does not undergo such a process. (As pointed out by Peter
Schroeder-Heister, this kind of ‘heterogeneity’ is not observed in occurrences
of multiple discharge in the derivation of e.g. the law of excluded middle.) So
perhaps there is something problematic about this particular kind of multiple
discharge, which is somewhat ‘incestuous’ in that a formula is assumed and then
‘applied’ to itself (or to its descendants) again.

[UPDATE: Shawn Standefer writes to draw my attention to a 2007 paper by Sue Rogerson in JPL that is highly relevant for the present discussion, 'Natural deduction and Curry's paradox'. Among other things, Rogerson reports (p. 159) that Fitch made a remark very similar to Schroder-Heister's:

He noticed that there was an unusual feature in the proof of the paradox: Namely, that the same formula is used both as a hypothesis for a subordinate proof and then again later as a minor premise in an application of àE.

She then goes on to discuss four different strategies considered by Fitch to deal with the phenomenon. Anyone interested in restrictions to contraction prompted by paradoxes must absolutely read this paper!]

Such observations might lead to
systems which are not contraction-free, strictly speaking, but where
contraction is restricted – hopefully on the basis of some robust principles
rather than an ad-hoc restriction ‘whenever needed’ (i.e. to block paradoxes).
This is indeed what Elia Zardini proposes in his recent RSL paper, namely an
independently motivated restriction of contraction. As I said before, Elia’s
proposal is to my mind the most compelling case for paradox-related contraction
restriction currently in the market.

A final worry for the proponents
of contraction-free systems is the extent of the loss incurred by the rejection
of contraction (a point made by Stephen Read). Without contraction, can we
still prove some of the results that we’ve learned to love and cherish, such as
Cantor’s or Gödel’s? If not, can we live without them? Ultimately, it may well
be that keeping a naïve conception of truth and ending up with an exceedingly
weak logic (if that’s indeed the case) might not be such a good idea after all:
the treatment may be more destructive than the disease itself. In other words:
can we do without contraction, and if yes, should we? At any rate, I for one
need paradox-unrelated reasons to convince me of giving up on contraction.

Philosophical explications of
central epistemic concepts such as inductive support, explanation, coherence or
conditional reasoning can often be effectively guided by experimentation.
However, due to their disciplinary background, most philosophers do not have
the in-house competence to effectively design such experiments, and to
operationalize and measure theoretical concepts. Vice versa, experimental psychologists interested in how people reason are
often not aware that longstanding or cutting-edge research in philosophy can
have implications for their own research targets, or find it difficult to
connect philosophical theories to their own research questions. On the other
hand, psychologists are usually equipped with strong theoretical, but also
practical knowledge about important strategies and pitfalls when it comes to
designing and implementing an experiment. Therefore we organize this workshop where both fields are brought together, and
where the methodology of operationalizing epistemic concepts is investigated
both from a theoretical and an empirical point of view. How should we devise
elicitation procedures for complex and potentially ambiguous epistemic notions?
How should we work out predictions that are precise enough to be put to
empirical test? Which experimental paradigms should be adopted in research on
human reasoning? How can we connect the philosophical interpretation of
epistemic concepts to the long-lasting empirical tradition in psychology?

Go here, here and here for the organization, abstracts and venue, respectively.

Anyone interested in attending can register by email to: tilps@uvt.nl.

The Priority Program New Frameworks of Rationality(SPP 1516) has been launched in 2010 by the Deutsche Forschungsgemeinshaft (DFG) and is designed to run for six years.
The goal of
the program is to overcome a long lasting lack of collaboration between
psychologists, philosophers and other research communities (such as AI) in order to develop new theoretical frameworks for the study of human
rationality. Go here for further details and here for an overview of the research projects funded within the Program.

Tuesday, 12 June 2012

I realize I'm probably pushing my luck a bit too far, but here's a bit of shameless self-promotion: my entry on medieval theories of consequence for the Stanford Encyclopedia of Philosophy is now online. Naturally, it is essentially a historical piece, but (I think) also quite relevant for contemporary debates on the notion of logical consequence. Here's a bit from the introduction:

Taken as a whole, medieval theories of consequence represent the first sustained attempt at adopting a sentential/propositional perspective since the Stoics in Greek antiquity, and — unlike Stoic logic, which had little historical influence — provide the historical background for subsequent developments leading to the birth of modern logic in the 19th century. Indeed, it will be argued that the medieval concept of consequentia (in its different versions) is the main precursor of the modern concept of logical consequence.

Sunday, 3 June 2012

Humpty Dumpty: Of course you don’t---till I tell you. I meant ‘there’s a nice knock-down argument for you!’

A: But ‘glory’ doesn’t mean ‘a nice knock-down argument’.

HD: When I use a word, it means just what I choose it to mean—neither more nor less.

A: But what you mean by ‘glory’ is different from what I mean by ‘glory’; which one is what ‘glory’ means?

HD: What does ‘means’ mean? ‘means’ can mean something persons mean and also something words mean. What a person means by a word is what the word means in the language they speak. What I mean by ‘glory’ is what ‘glory’ means in the language I speak; what you mean by ‘glory’ is what ‘glory’ means in the language you speak.

A: Does something "connect" the string of letters ‘glory’ and the meaning?

HD: Are there not two kinds of connection, not one? The meaning-relation for a language connects its words to their meanings. The cognizing relation connects minds to the language they speak.

A: Surely I connect the word and the meaning?

HD: I say that you---your mind---cognizes a structure, a bunch of syntax and meaning functions. You speak a language by cognizing these functions. I speak Humptese by cognizing its syntax and meaning functions; you speak Alicese by cognizing its syntax and meaning functions.

A: I see. The meaning relation has to be distinguished from the cognizing relation. And then, as Professor Saussure insists, the meaning relation is conventional. A word---a string of phonemes or letters---doesn’t mean anything ‘intrinsically’. Professor Tarski’s work seems to make this very clear.

HD: Some authors have attacked Professor Tarski for his clarity about the conventionality of the meaning-relation. The shock! For them, the meaning-relation has to be explained in terms of ‘natural facts’, the use of the string; the mental states involved in speech-acts producing the string; its role in reasoning; its causal connections to its referent; and so on. But these theories cannot even get the simplest fact about language---its conventionality---right! For the conventionality of meaning is explained by the fact that there is not just one meaning relation! For example, with two basic words, and a thousand possible meanings, there are one million meaning functions. When Professor Saussure says the meaning-relation is conventional, all he means is that each distinct function yields a distinct language. Change the function and you have a new langage. It seems to me that these authors confuse the meaning-relation (what a string means in a language) with the cognizing relation (what language a speaker speaks).

A: So, ... the meaning-relation is a mathematical relation. Its conventionality consists in that. I do like the view you advocate. But here is an interesting consequence: I could have spoken a language whose meaning function maps ‘cat’ to dogs. And if I had spoken that language, then I would not have been speaking the language I do in fact speak. For ‘cat’ means cats in Alicese, but means dogs in that language. And if ‘cat’ means dogs in a language, then that language cannot be Alicese. Not only is it a semantic fact that ‘cat’ mean cats in Alicese, it couldn’t have been otherwise: So, Alicese has an essential property: the property that ‘cat’ means cats in Alicese.

HD: Interesting, isn’t it, that conventionality and necessity are so closely linked?

A: But conventionality seems initially to be a matter of choice. So, ‘cat’ can mean one thing and mean another thing! But now I examine your theory, this is merely a multiplicity of mathematical possibilites. When we “choose”, our mind “chooses” one of these, by cognizing it---in a sense, speaking a language is a form of mathematical cognition; but, if this view is correct, then irrespective of which language one cognizes, what a string of phonenes means---relative to that meaning function---is necessary.

HD: For example, the string ‘gloobydooby’ doesn’t mean anything in Alicese! But, mathematically speaking, every word has a meaning relative to some language.

A: Yes, for example, any language in which ‘gloobydooby’ means Liverpool FC. Then it does mean something! But no one cognizes that language. So, another consequence is that the fact that there is no person who speaks a language in which ‘gloobydooby’ means Liverpool FC is no reason to deny there being such a language. Existir es no ser hablado!

HD: I thought Berkeley was Irish? But Latin is old-hat, I suppose. What shall we call these unspoken langages? Disembodied languages?

A: A second consequence of this view is this: if linguistic facts concerning disembodied languages are necessities and not contingencies, then linguistic facts cannot be discovered, or refuted, or explained by empirical science. A contingency cannot explain a necessity. How I happen to use a string cannot explain what it means! The usage somehow explains what I mean, but not what it means.

HD: How you use a word can help explain what language you happen to cognize.

A: Everyone speaks their own idiolect, which may be chopping and changing all the time. Maybe it can change in a nanosecond. Maybe you shift into different languages as the context changes. Why not? But what then is this thing called English? I suppose, it is a language mathematically defined by some grammar textbook, but is a language that no one speaks exactly. After all, not everyone has the same lexicon, the same meanings for words, the same pronunciations, the same pragmatic rules, and so on. If they all vary, even a tiny bit, then they are different. I suppose that, to use Professor Quine’s terminology, languages are individuated very finely: by exact sameness of phonetics, syntax, semantics and pragmatics. We might say that I speak Alice-English and you speak Humpty-English. But these aren’t instances of something more abstract, like Über-English. They are imperfect copies of each other.

HD: You mentioned Professor Quine. Do you recall his famous puzzle? A human rushes past the Mad Hatter who shouts out, ‘gavagai’. The Mad Hatter always tends to behave like this. Let us define Madhatterese to be the language that the Mad Hatter cognizes. Then, given his speech behaviour, what does the Madhatterese word ‘gavagai’ mean?

A: As I can now see, we should formulate the problem by first defining two languages L and L*, such that L maps ‘gavagai’ to humans, and L* maps ‘gavagai’ to undetached human parts (or to the image of the humans under some suitable proxy function). Then there is no question as to what the strings mean. It is a matter of definition that ‘gavagai’ means humans in L and means undetached human parts in L*. So, it really isn’t a puzzle about semantics. However, that said, we still do not know, on the basis of the Mad Hatter’s behaviour, which language Madhatterese is. We do not know if the Mad Hatter cognizes L or cognizes L*. But this is a problem concerning cognition, not semantics.

HD: All of these puzzles about semantics, for which Wittgenstein, Quine, Putnam and Kripke are rightly famous, can be reformulated in the same manner. Suppose that L maps 'number' to the numbers 0, 1, 2, ... while L* maps ‘number’ to elements of a non-standard model M of true arithmetic, then do number theorists cognize L or L*? Or suppose L assigns electrons to ‘electron’ while L* assigns protons to ‘electron’. Do scientists cognize L or L*? Suppose that the symbol ‘+’ means addition in L, and means quaddition in L*. Do we cognize L or L*? These are not problems in semantics at all! They are problems in cognitive science.

A: The problem doesn’t go away though, does it? For we have just moved the goalposts, from semantics to cognizing. For example, now we wish to know if the language that Professor Gowers cognizes is a language in which the meaning of ‘+’ is addition or a language in which its meaning is quaddition. And if the former, then how do we account for this?

HD: Like I said, earlier, when I use a word, it means just what I choose it to mean—neither more nor less!

A: And, in a nutshell, that is the following theory: an agent cognizes L just when the meaning of a word in L is exactly the meaning the agent assigns to that word. So have we solved the fundamental problem of twentieth century philosophy?

HD: Well, not really: for what does ‘the agent a assigns meaning m to word w’ mean?

A: Do I really have to analyse that relationship?

HD: Professor Putnam insists that it would involve “noetic rays”.

A: Well, I do assign meanings to words! I don’t know how, but surely I do.

HD: And you speak L if and only if L assigns to each word exactly what your mind assigns to it?

A: Yes.

HD: One thing that occurs to me is this. If you speak L and I speak L*, then we speak different languages; this makes communication occasionally non-optimal; should you change or should I change? Neither?

A: This is the question of collective linguistic normativity. There are only two reasons I can think of for changing my idiolect somehow. The first is to improve social co-ordination: then it’s easier for each of us to process incoming messages from others. The second is that my meanings---concepts---might be gerrymandered in the manner that has been discussed by Professors Goodman and Miller.

HD: I am not going to change my idiolect just to suit the demands of others! They can interpret me if they make a bit of an effort.

A: Despite your protestations, I bet you do modify your idiolect on some occasions. Several years ago, I noticed that experts in areas related to law, politics and epistemology always assign the concept UNBIASED to the string ‘disinterested’, whereas I, and quite a few other speakers, sometimes assign a different concept, NOT-BEING-INTERESTED to the string. When I noticed this, I deliberately changed my idiolect. I deferred to expertise in order to improve social co-ordination. In some cases, often with technical words like ‘isomorphism’, I’m sure that the concept I assign to the word is muddled and unclear. So, I defer to the expert, and modify my idiolect slightly.

HD: Well, I suppose in that sort of case, we decide to do that, yes. Isn’t this the topic of linguistic prescriptivism that many linguists get all huffed up about?

A: Yes: but they are being silly. Social co-ordination, expertise, and so on, all involve normativity. It is rational for humans to improve co-ordination and to share expertise. Still, I’m not sure about the other reason. It would require a kind of hierarchy or ordering of concepts: some concepts are more natural than others, while others, like GRUE, are gerrymandered. Perhaps that is right.

HD: If a language assigns some meanings which are gerrymandered, then the language itself would be somehow deficient. So, some languages would be "better" than others!

A: Yes, but it’s damn difficult to be convinced that this is right. Maybe it’s connected to simplicity somehow. But it’s very hard to see how to make sense of ideas like concepts being more natural or the world being simpler.

HD: Anyway, good luck with all that, Alice! Disembodied languages, meaning-functions, noetic rays and natural concepts! Let’s call your cognizing function the noetic-function. Speaking a language L involves the equivalence of a noetic-function and L’s meaning-function. Do you think you can get a funding agency to support that? Your research career is ruined.

A: Why should I care?

HD: You’re right.

A: So, the question is how our noetic rays can make words mean so many different things.

HD: The question is which is to be master---that’s all.

A: But with that, Mr Dumpty, I disagree!

[This dialogue is based on ideas from a couple of talks I've given over the last few years. One, "Meaning, Use and Modality" in Madrid in 2008; another, "Cognizing a Language", at the Edinburgh Linguistics Society in October 2010; and a related talk, "Deflationism and Representationalism", I gave in Vienna and Munich in March 2012.]

From October 2012 the Faculty of Philosophy, Philosophy of Science and Study of Religion at LMU Munich is going to run an international MA program in Logic and Philosophy of Science (next to other MA degrees which will be starting at the same time, including a general MA in Philosophy).

LMU has a long-standing tradition in philosophy of science and logic that reaches back to the time of Wolfgang Stegmüller and Kurt Schütte. In recent years, this tradition has been revived by establishing a new chair in logic and philosophy of language (held by Hannes Leitgeb) and by founding the Munich Center for Mathematical Philosophy (MCMP) which is devoted to the application of logical and mathematical methods in philosophy. Hannes Leitgeb was awarded an Alexander von Humboldt Professorship by the German Alexander von Humboldt Foundation in 2010, and in April 2012 it was announced that another Alexander von Humboldt Professorship will be awarded to Stephan Hartmann who will be moving to LMU by autumn of this year in order to take up the chair in philosophy of science at LMU. Leitgeb and Hartmann will also be co-directing the new MA program. For a list of people working at LMU in logic, philosophy of science, and adjacent areas, please see here and here. gives a good overview of some of the research that is presently done here. Overall, the Faculty of Philosophy, Philosophy of Science and Study of Religion at LMU is one of the largest in the German-speaking world, it covers all areas of philosophy, and it has a strong interdisciplinary orientation towards areas such as physics, neuroscience, mathematics, statistics, linguistics, computer science, and more.

Here are some details about our MA in Logic and Philosophy of Science:

Language (of program and courses): English.Start date: In the coming winter semester, teaching commences on October 15th, 2012.Duration: The MA can be done within one year (two semesters, 60 ECTS) or within two years (four semesters, 120 ECTS), depending on one's preferences, background, and previous education. The MA is a self-standing degree, but of course it can also serve as preparation for doctoral research.Structure: In each semester, all students in the program attend a dedicated compulsory MA seminar (the "Master Colloquium"); over and above that, right until their final semester, they are choosing units from a broad range of additional courses in logic, philosophy of science, and related areas. The final semester is devoted to writing an MA thesis.Community: We host a lively community of university faculty, MCMP fellows, students, and visitors. All MA students will be able to join the great number of academic activities at the university in general and at the MCMP in particular, including two weekly research seminars in logic, philosophy of science, and mathematical philosophy for speakers from outside, a weekly internal work-in-progress seminar, reading groups, workshops, and conferences. For a list of current activities. We have strong ties to institutions of a similar kind, whether on an international scale or in Munich, and we regularly host visitors who do their research at our Center or who teach here. Additionally, the journal Erkenntnis is based at the MCMP. More information for international students about studying at LMU can be found here.Entry requirements: Academically, an average mark in one's undergraduate studies of at least 2,0 in the German system is required (which corresponds to at least an upper second-class honours degree in the British system or the international equivalent thereof). It is possible to apply for a place in the program even if one does not yet have finished one's undergraduate studies: in such a case we would make a conditional offer, accordingly. The program is not just open to philosophy and logic undergraduates but also to undergraduates from relevant scientific disciplines, such as mathematics, physics, biology, chemistry, neuroscience, computer science, engineering, economics, linguistics, psychology, cognitive science, the social sciences or related disciplines.
If your first language is not English and you do not have a degree from an English-speaking university, you will need to supply us with evidence of your language skills as far as speaking and writing in English is concerned: we demand at least a 6.5 in all IELTS bands (or equivalent).Fees and financial support: Every student at LMU has to pay EUR 500 per semester for their studies. We will be able to support selected applicants to our MA program in Logic and Philosophy of Science with a limited number of a tax-free monthly stipends of EUR 1000 for the whole period of their studies.Continuing after the MA: The MA program can be continued by entering our PhD program. The MCMP regularly advertises Doctoral Fellowships to which students in our MA program may apply.Proviso: We should add that, since the MA program is new, it still needs to be confirmed officially by the senate of the LMU (amongst others)

Application Procedure:
We will accept applications until

July 15th, 2012

but we strongly recommend to apply before that date.
First of all, please submit your application electronically to

office.leitgeb@lrz.uni-muenchen.de

The following files are required:

(1) A cover letter in which you explain why you would like to join the program.
(2) A CV (including the list of courses that you have taken as an undergraduate).
(3) A copy of your undergraduate final grade certificate.
(4) A seminar paper or published article that you have written which is open in terms of its subject, but which should give evidence of clarity of thought, systematicity, logical argumentation, and an awareness of methodological questions, which are all particularly relevant to our MA program.
(5) Two letters of reference, which should also address your special potential in the very areas that are covered by our MA program.
(6) Proof of English language proficiency (IELTS or equivalent), in case your first language is not English and you do not have a degree from an English-speaking university.

If necessary, applicants may also be interviewed. If you have questions about that part of the application process, please send them to office.leitgeb@lrz.uni-muenchen.de as well.

Secondly, and in addition, please apply simultaneously to the International Affairs Office at LMU which will check for general requirements that concern Master studies at LMU in general. Here you can download the set of application documents for Master degrees at LMU. There you will also find information about which documents to submit to the International Affairs Office, how to submit them, and whom you can contact about this other part of the application process in case of questions.

Contact: If you have any questions about the program or the application process, please send a message to office.leitgeb@lrz.uni-muenchen.de.